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Difference between revisions of "Diagonal matrix"

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I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form
 
I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form
  
$$\begin{pmatrix}a_1&0&\dots&0\\0&a_2&\dots&0\\\dots&\dots&\dots&\dots\\0&\dots&\dots&a_n\end{pmatrix},$$
+
$$\begin{pmatrix}a_1&0&\cdots&0\\0&a_2&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&\cdots&\cdots&a_n\end{pmatrix},$$
  
 
where the $a_i$ are elements of $K$.
 
where the $a_i$ are elements of $K$.
  
 
See also: [[Defective matrix]].
 
See also: [[Defective matrix]].
 
  
 
====References====
 
====References====

Latest revision as of 03:37, 25 February 2022

2020 Mathematics Subject Classification: Primary: 15B [MSN][ZBL]

quasi-scalar matrix

A square matrix in which all entries — with the possible exception of the elements on the main diagonal — are zero.


Comments

I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form

$$\begin{pmatrix}a_1&0&\cdots&0\\0&a_2&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&\cdots&\cdots&a_n\end{pmatrix},$$

where the $a_i$ are elements of $K$.

See also: Defective matrix.

References

How to Cite This Entry:
Diagonal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Diagonal_matrix&oldid=52115
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article